Modeling and Analysis of Temporal Failure and Degradation Behavior of Critical Infrastructure Systems

In this paper, we present an approach for modeling and analyzing the temporal failure and degradation behavior of critical infrastructure systems (CISs) using advanced temporal database management systems. We classify the possible failure and/or degraded performance of CISs into different temporal categories, namely, crisp or exact intervals, nonvanishing imprecise intervals and vanishing imprecise intervals. The three temporal operators: Union (OR), Overlap (AND) and Not are extended to operate on the above categories of precise and imprecise intervals. The temporal operators are used recursively to capture the fault tolerance topology of CIS. For example, if a component of CIS has built-in redundancy for fault tolerance, the fault behavior of this component propagates to the outside only when all the redundant units of this component fail simultaneously. In this case, the failure temporal expressions of the redundant units are joined by temporal Overlap operators to indicate that the failure of the composite component is contingent on the failure of all units. We briefly show how query languages with temporal extensions can be used to obtain useful answers for time-related queries and retrieve useful information about the exact and potential time points for degraded modes of operation. The storage overhead of incorporating the imprecise intervals in a temporal database is analyzed.